TRIGONOMETRYFinal Review

1. APPROXIMATE SEC 320°

.77 .90 1.1 1.3

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EXCELLENT!

2. IF SEC =2 FIND TAN .

√3/2 ½ √3 2

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FABULOUS!

3. FIND TAN 7Π/4

.10 -.10 1 -1

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GREAT JOB!

4. FIND A POSITIVE AND NEGATIVE ANGLE COTERMINAL TO 5Π/3 (IN RADIANS).

-11π/3 and π/3 -π/3 and 11π/3 -11π/3 and 11π/3 -π/3 and π/3

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WAY TO GO!

5. FIND THE REFERENCE ANGLE FOR 13Π/6.

π/6 or 30° π/3 or 60° -π/6 or -30° -π/3 or -60°

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ROCK ON!

6. FIND ALL VALUES BETWEEN 0 AND 360° WHERE SIN =-1/2

150° and 210° 240° and 320° 210° and 330° 150° and 330°

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WOW!

7. FIND THE APPROXIMATE ARC LENGTH IF THE CENTRAL ANGLE IS 40° AND THE RADIUS OF THE CIRCLE BEING INTERCEPTED IS 5 UNITS.

1.75 3.49 5.25 200

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SUPER!

8. a=4 b=3 and c=5. Find A.

.64 degrees .93 degrees 36.9 degrees 53.1 degrees

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YOU ROCK!

9. B=34°20’ C=90° and c=8. Find b.

1.78 4.5 6.6 14.8

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MAGNIFICENT!

10. A=32° C=90° and b=5. Find a.

2.00 3.12 4.24 8.00

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MARVELOUS!

11. A=40° B=80° and c=4. Find b.

1.39 2.97 4.55 6.13

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OUTSTANDING!

12. SIMPLIFY TANACOS²A

sinAcosA cosAtanA sin²A tan²A

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AWESOME!

13. SIMPLIFY SINX+COSXTANX.

sinxcosx 2cosx 2tanx 2sinx

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HOORAY!

14. SIMPLIFY TANXCSCX

sinx cosx secx cotx

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GREAT JOB!

15. WHICH ONE IS EQUIVALENT TO 1+TAN SEC

1+csc 1+cot 2sincos sin+cos

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WAY TO GO!

16. WHICH IS EQUIVALENT TO 1+SEC²XSIN²X

csc²x sec²x tan²x cot²x

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GREAT JOB!

17. FIND THE DOMAIN AND RANGE FOR Y=CSCX

Domain: all reals not equal to πk; Range: (-∞,-1][1,∞)

Domain: (-∞,-1][1,∞); Range: all reals not equal to πk

Domain: all reals; Range: [-1,1] Domain: all reals not equal to π/2+π

k; Range: (-∞,-1][1,∞)

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OUTSTANDING!

18. NAME THE AMPLITUDE AND PERIOD AND PHASE SHIFT FOR Y=COS(2+Π)

Amplitude: 2, period: π, and phase shift π/2 right

Amplitude: 2, period: π/2, and phase shift π/2 left

Amplitude: 1, period: π/2, and phase shift π/2 right

Amplitude: 1, period: π, and phase shift π/2 left

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KEEP UP THE GREAT WORK!

19. NAME THE PERIOD AND PHASE SHIFT FOR Y= TAN(-Π/2)

Period π and phase shift π/2 right Period π and phase shift π/2 left Period 2π and phase shift π/2 right Period 2π and phase shift π/2 left

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RIGHT ON!

20. NAME THE AMPLITUDE AND PERIOD AND PHASE SHIFT FOR Y=-3COS(4X+Π/2)

Amplitude 3, period π/4, and phase shift π/2 left

Amplitude 3, period π/4, and phase shift π/8 left

Amplitude 3, period π/2, and phase shift π/2 left

Amplitude 3, period π/2, and phase shift π/8 left

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SO PROUD OF YOU!

21. FIND THE AREA OF A CIRCULAR SEGMENT TO THE NEAREST TENTH IF THE MEASURE OF ITS CENTRAL ANGLE IS 220° AND THE MEASURE OF ITS RADIUS IS 8.5 UNITS.

935 units² 138.7 units² 7947.5 units² 10,021.8 units²

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EXCELLENT!

22. FIND ALL VALUES OF X WHERE SIN X = 1.

270° + 360k 180° + 360k 90° +360k 360k

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FABULOUS!

23. EVALUATE COS(SIN-11/2). ASSUME X IS IN QUADRANT 1.

√(3)/2 √3 2 √(3)/3

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GREAT JOB!

24. FIND THE VALUES OF X IN THE INTERVAL [-180˚, 180˚] THAT SATISFY THE EQUATION SIN X = -1/2.

30˚ and 150˚ 60˚ and 300˚ -60˚ and -300˚ -30˚ and -150˚

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WAY TO GO!

25. EVALUATE COS(TAN-11) + SIN(TAN-1√3)

(X IS IN QUADRANT I)

1 + √(3)/2 2 + √(2)/2 √(2)/2 + √(3)/2 √(3)/3 + √3

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ROCK ON!

26. WRITE AN EQUATION OF THE COSINE FUNCTION WITH AMPLITUDE 5, PERIOD 540˚ AND PHASE SHIFT 135˚ TO THE LEFT.

Y= 5 cos (2/3x – л/2) Y= 5 cos (2/3x + л/2) Y= 5 cos (1/2x – л/4) Y= 5 cos (1/2x + л/4)

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WOW!

27. EXPRESS COS 510˚ AS A FUNCTION OF AN ANGLE IN QUADRANT I

-cos 30˚ cos 30˚ -cos 60˚ cos 60˚

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GREAT JOB!

28. WHICH EQUATION IS A TRIG IDENTITY?

cos